Hello I'm a Australian living in Germany in the mountains, we go hiking regularly with our 4 year old he has been hiking for a year now and can hike 3-5 hours actually he runs up mountains and has been up to 1800mts. We just brought a gondola pass that give us access to 20 gondolas in the area so now we are going from peak to peak, now our son is a runner and doesn't always listen( not unusual really) but I'm a bit worried he might have a fall and some of the trails are narrow, so just wanted to know if anybody puts a harness on there child when hiking. I'm starting to think i should but just wanted to know people's thoughts.
Cheers

Kids generally don't run wildly when there is an obvious danger like a cliff. If the path is so narrow that an accidental stumble would be dangerous, you can hold his hand.

Was your idea to attach a leash to the harness? That won't work to stop a vertical fall. He might happen to slip on a grassy slope that's just the right steepness that holding a leash in your hand will make the difference, but that's a gamble. Either trust him not to fall, or hold him so he can't fall, or use a full-on rope system with a proper anchor. In-between measures don't work.

A harness without a leash does have its uses. I used one when taking my then-three-year-old along on steep approaches to climbs. It provided secure hand-holds which were useful when passing him to others to get up or down boulders that were too big for him.

Mt wife's family always put harness on kids, because they tended to fall off rough shorelines into the water, etc. The harnesses they used were sort of chest harnesses, with an attachment in back. Most are made for kids 2-3, you should adjust for weight

Absolutely! And this is an excellent kids harness: https://www.petzl.com/US/en/Sport/Harnesses/SIMBA. Easy to put on, and ties in securely. And I would certainly keep a little one "tied in", you never know when they're going to get distracted and go take a look at something, slip on a loose rock/stick, or whatever little kids do while they're learning.